# Wine tasting from Prob and Stat for Engineering and the Sciences by Devore

Since the taster has a 1/3 chance of randomly selecting the wine that is different from the other two, and you either get it right or wrong, we have a binomial distribution with p=.333 and q=.667. Out of 855 tasting trials, by random chance the mean should be 855/3=285. The null hypothesis should then be $H_{0}:\mu=285$ with $H_{a}:\mu>285$.
The closest I can come to a standard deviation is 346-285=61 and $61^2$ is 3721 divided by 854 gives 4.36.
Now take $\frac{346-285}{\frac{3721}{\sqrt{855}}}$=.479=z $\Phi(.479)$=.6844 P-value=2(1-.6844)=.6312.